Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C23 |
| direct product | #2141×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×D8 |
| commutator | C8 | C22×C4×C151 |
| Frattini, cosocle | C2×C8 | C23×C151 |
| prime radical | C23×C151 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×C8×C151 ◁ G | |
220 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 187 points:
(1,2,3,4)(5,6)(7,16)(8,13)(9,22)(10,26)(11,15)(12,18)(14,24)(17,30)(19,36)(20,33)(21,31)(23,29)(25,32)(27,34)(28,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187);(5,7,11,20)(6,12,15,28)(8,19,10,17)(9,23,25,34)(13,29,26,27)(14,30,31,36)(16,32,33,22)(18,21,35,24);(5,8,11,10)(6,13,15,26)(7,17,20,19)(9,21,25,24)(12,27,28,29)(14,22,31,32)(16,30,33,36)(18,34,35,23)4832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C151×#12648, C151×#12742, C151×#12751, … |
| maximal normal subgroup of | C151×#12648, C151×#12742, C151×#12751, … |
| maximal quotient of | C151×#11594, C151×#11650, C151×#11662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 873);